Celestial swingers

By David Appell

TAKE three big rocks into space and lob them in random directions. Where do
they go? This is an ancient problem in celestial mechanics, the question of how
a collection of three or more objects will move under their mutual gravitational
attraction. You have to solve it in order to predict how bodies in the Solar
System move—where the Moon will be in a million years, for example. And
the answer is . . . well, nobody really knows.

The fact that there is no solution to the “three-body problem” means that we
are reduced to a kind of educated guess. Orbits aren’t always simple circles or
ellipses. Without a complete and precise formula that says exactly what the Moon
will do, we have to rely on approximations—computer calculations that
predict orbits superbly in the short term, but eventually become so uncertain
that we have to shrug our shoulders and give up.

In the past two years, however, an unexpected collection of solutions to this
ancient puzzle has come tumbling out of abstract mathematical space, revealing
beautiful, looping orbits where as many as 800 bodies dance around one another.
Somewhere out there, perhaps even in our own Galaxy, troops of stars may be
following some of these weird dances.

So what is the problem with the three-body problem? It ought to be simple, as
there are just two basic ingredients, both formulated by Isaac Newton. The first
is his equation of motion, which tells you how a mass accelerates if you apply a
force to it. The second is his law of universal gravitation, which …

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